Question

Apply the Pythagorean Theorem to find the length between (2, 5)
and (7, 3)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

29
29

4.58
4.58

5.39
5.39

2.65
2.65

Answer 1

To find the length between the points \((2, 5)\) and \((7, 3)\), we can use the distance formula, which is derived from the Pythagorean Theorem:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\). Now, let's plug in the values:

\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]

Calculating inside the parentheses:

\[
d = \sqrt{(5)^2 + (-2)^2}
\]

Calculating the squares:

\[
d = \sqrt{25 + 4}
\]

Adding them together:

\[
d = \sqrt{29}
\]

Now, calculate \(\sqrt{29}\):

\[
\sqrt{29} \approx 5.385
\]

Rounding to the nearest hundredth gives:

\[
5.39
\]

So, the length between the points \((2, 5)\) and \((7, 3)\) is approximately **5.39**.